data.frame in long format, computes,
for a single set of smoothing parameters, smooths of the
response, possibly along with growth rates calculated from the
smooths.Uses smoothSpline to fit a spline to the values
of response for each individual and stores the fitted
values in data. The degree of smoothing is controlled by the
tuning parameters df and lambda, related to the
penalty, and by npspline.segments. The smoothing.method
provides for direct and logarithmic smoothing.
The Absolute and Relative Growth Rates ( AGR and RGR) can be computed
either using the first derivatives of the splines or by differencing
the smooths. If using the first derivative to obtain growth rates,
correctBoundaries must be FALSE. Derivatives other than the
first derivative can also be produced. The function
byIndv4Times_GRsDiff is used to obtain growth rates by
differencing.
The handling of missing values in the observations is controlled via
na.x.action and na.y.action. If there are not
at least four distinct, nonmissing x-values, a warning is issued and
all smoothed values and derivatives are set to NA.
The function probeSmooths can be used to investgate the effect
the smoothing parameters
(smoothing.method, df or
lambda) on the smooth that results.
byIndv4Times_SplinesGRs(data, response, response.smoothed = NULL,
individuals = "Snapshot.ID.Tag", times,
smoothing.method = "direct", smoothing.segments = NULL,
spline.type = "NCSS", df=NULL, lambda = NULL,
npspline.segments = NULL,
correctBoundaries = FALSE,
rates.method = "differences",
which.rates = c("AGR","RGR"),
suffices.rates = NULL, sep.rates = ".",
avail.times.diffs = FALSE, ntimes2span = 2,
extra.derivs = NULL, suffices.extra.derivs=NULL,
sep.levels = ".",
na.x.action="exclude", na.y.action = "trimx", ...)A data.frame containing data to which has been
added a column with the fitted smooth, the name of the column being
the value of response.smoothed. If rates.method is
not none, columns for the growth rates listed in
which.rates will be added to data; the names each of
these columns will be the value of response.smoothed with
the elements of which.rates appended.
When rates.method is derivatives and
smoothing.method is direct, the AGR is obtained
from the first derivative of the spline for each value of times
and the RGR is calculated as the AGR divided by the
value of the response.smoothed for the corresponding time.
When rates.method is derivatives and
smoothing.method is logarithmic, the RGR is
obtained from the first derivative of the spline and the AGR
is calculated as the RGR multiplied by the corresponding
value of the response.smoothed.
If extra.derivs is not NULL, the values for the
nominated derivatives will also be added to data; the names
each of these columns will be the value of response.smoothed
with .dvf appended, where f is the order of the
derivative, or the value of response.smoothed
with the corresponding element of suffices.deriv appended.
Any pre-existing smoothed and growth rate columns in data will be
replaced. The ordering of the data.frame for the times
values will be preserved as far as is possible; the main difficulty
is with the handling of missing values by the function merge.
Thus, if missing values in times are retained, they will occur at
the bottom of each subset of individuals and the order will be
problematic when there are missing values in y and
na.y.action is set to omit.
A data.frame containing the column to be smoothed.
A character giving the name of the column in
data that is to be smoothed.
A character specifying the name of the column
containing the values of the smoothed response variable, corresponding
to response. If response.smoothed is NULL, then
response.smoothed is set to the response to which is added
the prefix s.
A character giving the name(s) of the
factor(s) that define the subsets of response
that correspond to the response values for an individual
(e.g. plant, pot, cart, plot or unit) that are to be smoothed
separately. If the columns corresponding to individuals are
not factor(s) then they will be coerced to
factor(s). The subsets are formed
using split.
A character giving the name of the column in
data containing the times at which the data was
collected, either as a numeric, factor, or
character. It will be used as the values of the predictor
variable to be supplied to smooth.spline and in
calculating growth rates. If a factor or
character, the values should be numerics stored as characters.
A character giving the smoothing method
to use. The two possibilites are (i) "direct", for directly
smoothing the observed response, and (ii) "logarithmic", for
smoothing the log-transformed response and then
back-transforming by taking the exponentional of the fitted values.
A named list, each of whose components
is a numeric pair specifying the first and last values of an
times-interval whose data is to be subjected as an entity to smoothing
using splines. The separate smooths will be combined to form a whole
smooth for each individual. If get.rates is TRUE,
rates.method is differences and ntimes2span is 2,
the smoothed growth rates will be computed over the set of segments;
otherwise, they will be computed within segments.
If smoothing.segments is NULL, the data is not
segmented for smoothing.
A character giving the type of spline
to use. Currently, the possibilites are (i) "NCSS", for natural
cubic smoothing splines, and (ii) "PS", for P-splines.
A numeric specifying, for natural cubic smoothing splines
(NCSS), the desired equivalent number of degrees of freedom of the
smooth (trace of the smoother matrix). Lower values result in more smoothing.
If df = NULL, the amount of smoothing can be controlled by setting
lambda. If both df and lambda are NULL, smoothing
is controlled by the default arguments for smooth.spline, and any
that you supply via the ellipsis (...) argument.
A numeric specifying the positive penalty to apply.
The amount of smoothing decreases as lamda decreases.
A numeric specifying, for P-splines (PS),
the number of equally spaced segments between min(times) and max(times),
excluding missing values, to use in constructing the B-spline basis for the
spline fitting. If npspline.segments is NULL, npspline.segments
is set to the maximum of 10 and ceiling((nrow(data)-1)/2) i.e. there will
be at least 10 segments and, for more than 22 times values, there will be
half as many segments as there are times values. The amount of smoothing
decreases as npspline.segments increases. When the data has been
segmented for smoothing (smoothing.segments is not NULL),
an npspline.segments value can be supplied for each segment.
A logical indicating whether the fitted spline
values are to have the method of Huang (2001) applied
to them to correct for estimation bias at the end-points. Note that
spline.type must be NCSS and lambda and deriv
must be NULL for correctBoundaries to be set to TRUE.
A character specifying the method to use in
calculating the growth rates. The possibilities are
none, differences and derivatives.
A character giving the growth rates that are
to be calculated. It should be a combination of one or more of
"AGR", "PGR" and "RGR".
A character giving the characters to be
appended to the names of the responses to provide the names of the
columns containing the calculated growth rates. The order of the
suffices in suffices.rates should correspond to the order
of the elements of which.rates. If NULL, the values
of which.rates are used.
A character giving the character(s) to be used
to separate the suffices.rates value from a response
value in constructing the name for a new rate. For no separator,
set to "".
A logical indicating whether there is an
appropriate column of times diffserences that can be used as
the denominator in computing the growth rates. If TRUE, it will
be assumed that the name of the column is the value of times
with .diffs appended. If FALSE, a column, whose
column name will be the value of times with .diffs
appended, will be formed and saved in the result, overwriting any
existing columns with the constructed name in data. It will
be calculated using the values of times in data.
A numeric giving the number of values in
times to span in calculating growth rates by differencing.
Each growth rate is calculated as the difference in the values of
one of the responses for pairs of times values that
are spanned by ntimes2span times values divided by
the difference between this pair of times values. For
ntimes2span set to 2, a growth rate is the
difference between consecutive pairs of values of one of the
responses divided by the difference between consecutive
pairs of times values.
A numeric specifying one or more orders of derivatives
that are required, in addition to any required for calculating the growth
rates. When rates.method is derivatives, these can be
derivatives other than the first. Otherwise, any derivatives can be
specified.
A character giving the characters to be
appended to response.method to construct the names of the derivatives.
If NULL and the derivatives are to be retained, then .dv
followed by the order of the derivative is appended to
response.method
.
A character giving the separator to use when the
levels of individuals are combined. This is needed to avoid
using a character that occurs in a factor to delimit
levels when the levels of individuals are combined to identify
subsets.
A character string that specifies the action to
be taken when values of x, or the times, are NA.
The possible values are fail, exclude or omit.
For exclude and omit, predictions and derivatives
will only be obtained for nonmissing values of x.
The difference between these two codes is that for exclude the returned
data.frame will have as many rows as data, the
missing values have been incorporated.
A character string that specifies the action to
be taken when values of y, or the response, are
NA. The possible values are fail, exclude,
omit, allx, trimx, ltrimx or
rtrimx. For all options, except fail, missing
values in y will be removed before smoothing.
For exclude and omit, predictions
and derivatives will be obtained only for nonmissing values of
x that do not have missing y values. Again, the
difference between these two is that, only for exclude
will the missing values be incorporated into the
returned data.frame. For allx, predictions and
derivatives will be obtained for all nonmissing x.
For trimx, they will be obtained for all nonmissing
x between the first and last nonmissing y values
that have been ordered for x; for ltrimx and
utrimx either the lower or upper missing y
values, respectively, are trimmed.
allows for arguments to be passed to smooth.spline.
Chris Brien
Eilers, P.H.C and Marx, B.D. (2021) Practical smoothing: the joys of P-splines. Cambridge University Press, Cambridge.
Huang, C. (2001) Boundary corrected cubic smoothing splines. Journal of Statistical Computation and Simulation, 70, 107-121.
smoothSpline, probeSmooths, byIndv4Times_GRsDiff,
smooth.spline, predict.smooth.spline,
split
data(exampleData)
#smoothing with growth rates calculated using derivates
longi.dat <- byIndv4Times_SplinesGRs(data = longi.dat,
response="PSA", response.smoothed = "sPSA",
times="DAP",
df = 4, rates.method = "deriv",
suffices.rates = c("AGRdv", "RGRdv"))
#Use P-splines
longi.dat <- byIndv4Times_SplinesGRs(data = longi.dat,
response="PSA", response.smoothed = "sPSA",
individuals = "Snapshot.ID.Tag", times="DAP",
spline.type = "PS", lambda = 0.1,
npspline.segments = 10,
rates.method = "deriv",
suffices.rates = c("AGRdv", "RGRdv"))
#with segmented smoothing and no growth rates
longi.dat <- byIndv4Times_SplinesGRs(data = longi.dat,
response="PSA", response.smoothed = "sPSA",
individuals = "Snapshot.ID.Tag", times="DAP",
smoothing.segments = list(c(28,34), c(35,42)),
df = 5, rates.method = "none")
Run the code above in your browser using DataLab